Splitting-type method for systems of variational inequalities

We consider a system of variational inequalities with multivalued mappings, which can be viewed as an extension of constrained primal–dual variational inequalities. We propose to solve this problem with the help of a class of combined relaxation and splitting methods. We establish a convergence result for these methods for the case where the dual system is solvable. We also give several examples of applications to saddle point problems in optimization, Nash equilibrium problems in game theory, and economic equilibrium problems.